Tom,

Your essay is as usual, a Tour de Force of highly condensed mathematical acumen. I've given it two readings and find much I have to learn more about. In general, however, the theme is clear and is concisely stated where you say,

"- if nothing exists in reality save random events, there is no natural correspondence of mathematics to physics."

I was impressed by your carefully avoiding a philosophic character of argument, and keeping matters very much on message of the nuts and bolts of math needing an independent yet true correspondence to physics being about that which is physical, without any ad hoc contrivance of the math to match the physical empiricism. The point you make about QM conventionally constraining measurement space to the Bloch sphere provides a conceptual 'visual aid' when contemplating that a continuous function must exist in metamorphizing a spherical (curved) space and a cubic (flat) space. The 1500 year old edifice Hagia Sophia comes to mind, and with it the geometric sense of strength in physical spacetime.

I think you have made a good argument that what distinguishes where math is exemplary of physical reality is where there is continuity, and your approach to the Contest Topic by way of probabilities is challenging. I still have my sticky note of your conjecture and think it has a good fit in your presentation. Good Luck, don't let the back-biters bug. jrc

    Hi John,

    It's been a constant source of pleasure and delight to me, that you truly get what I'm saying. And I don't just mean the words -- I mean the essential message of a committed rationalist.

    Thank you and all best,

    Tom

    Tom,

    The pleasure has been mine, I can only understand rationalists and have learned much from you. I was especially pleased to learn from your essay the logic of Euler's equation. It never bothered me that he once said that any first rate mathematician would immediately see it, because I've never imagined myself a mathematician. But it has pestered me that I couldn't see it. Forest for the trees sort of thing, I was hung up on the numerical values. The manner you introduced it in your argument displays the simple logic both geometrically of a 1pi rotation, and algebraically of 'e'; it is the real function of each, not the arithmetic values that are at work! My horizons have been greatly enlarged. Thank-you very much. jrc

    Hi John,

    I think it was Gauss who said that. You're right, though -- analysis is far more compelling as a physical language than arithmetic. We actually experience geometry, as 3-dimension beings with 4-dimension brain-minds. Einstein in fact made what seems a mystical statement on first blush -- that he experienced relativity kinesthetically. Rotation, though, is a physical sense in more basic terms than a simple discrete point or line.

    Best,

    Tom

      Dear Mr. Fisher,

      I will entertain your point if you communicate it to me telepathically -- i.e., without using words, pictures or sign language, all of which are abstractions.

      Can you do that?

      Best,

      Tom

      Tom,

      I think the last minute submission of your essay may have gotten lost in the flood. Not necessarily a bad thing given past experience with speculators whom seem to think the object is a sparring contest of pet peeves, and the quantum maniacal denial of realism.

      I've never had a fascination with probabilities, so I need taken by the hand and shown so to speak. Could you briefly explain the sqrt2 lower bound on information? Also I'm a little fuzzy on your construction of M=4P, though I see how it is necessary that four physical states must evolve from the possible outcomes of pairs of coin tosses.

      Perhaps in a while there will be comments by others with proficiency in both classical and quantum probabilities to promote a learning experience. Best jrc

      John,

      Haters gonna hate. :-) I know from past experience that a couple of knuckleheads will knock a new entry down without reading it, just to try and suppress competition. Along with some others, I have been critical of the 'peer' voting system; it does no service to science that the peer group is limited only by one's capacity to use a keyboard.

      You write, "Could you briefly explain the sqrt2 lower bound on information?"

      It's as old as the first proof of Pythagoras's theorem, which actually may be even older than the Pythagoreans. Independent of the respective values for the lengths of legs in a given right triangle, the hypotenuse gives up no rational information about its own length with the exception of square integrable values -- even though sqrt2 is an algebraic number, i.e. the solution to an algebraic equation, it is defined only in terms of the nonzero endpoints of its pair of legs. Take the smallest real integral result of a^2 b^2 = c^2: 3^2 4^2 = 5^2:

      It's pretty obvious that 9 16 = 25. The values are square integrable. If measurements consisted only of square integrable results, the theorem would be uninteresting. Not only are real 2-dimension measures generalized to every pair of straight lines forming a right triangle, however, all information of the hypotenuse is reduced to an irrational number. If one asks the question: what is the exact length of the hypotenuse? -- there will be no exact answer. It can only be given in terms of the squares of each side of the triangle; the area is bounded, even though the endpoints of sqrt2 are not.

      This mathematics only becomes interesting, when raised to a four-dimension Pythagorean theorem (Riemannian geometry). That's beyond the scope of my essay.

      "Also I'm a little fuzzy on your construction of M=4P, though I see how it is necessary that four physical states must evolve from the possible outcomes of pairs of coin tosses."

      Remember, we are talking about relativity. The coefficient 4 is a constant that includes the observer as a physical state, just as the constant c^2 in Einstein's equation defines rest energy directly proportional to mass. The whole set of coin tosses for all time is encoded in the relation -- as Tegmark says, his MUH will be refuted if there is fundamental randomness in the universe. M = 4P tells us that there is no fundamental randomness. As I show in the essay, only pairwise initial conditions have a definite Truth Value -- so there is only classical, i.e., binary, probability and no fundamental randomness.

      Best,

      Tom

      Dang it. My posts keep appearing outside the thread that I thought I placed them in. Sorry.

      Tom

      Dear Tom

      I liked your quote of John Barrow's interpretation of Gödel: "if mathematics is a religion, it is the only religion that can prove it is a religion". As I discussed in my 2012 essay I have found such a proof. The problem is that we have a religion that doesn't want to admit the truth that it is a religion. The expedient way of dealing with such a proof is to deny it exists. As you discuss in your essay, Bell-like analysis on the border between maths and physics is not straightforward. It is possible to make implicit assumptions that undermine the generality of the result - as you are saying about Bell. In my essay I adopt a physics realism approach to the same questions on the basis that the true physical dynamics is hidden by simply being too fast for any experiment to measure. This option isn't covered by Bell, and I find that quantum theory results can be reproduced. Where my essay was cut short by the word count, is on the issues of probability, locality and non-locality you discuss in your essay. I would be interested in your view of my new approach to Bell-like analysis, and what it implies for probability and non-locality.

      Regards

      Michael Goodband

        Dear Tom,

        I am so sorry that you apparently cannot understand written English.

        Remedial courses are available at very low cost.

        Congenially,

        Joe Fisher

          Thanks, Joe. It's just all those abstractions that confound me. Words, you know.

          Tom,

          I must confess that I have not yet mastered the erudite arguments you pose, but knowing a small bit about Tegmark's MUH, I wondered about the "independence of humans" aspect of the ERH. Current physics theories are the math equations and structures describing the theory and their concepts, thus explaining the connections to our observations. The equations are built by humans and are their baggage. I don't see the separation.

          My "Connection of Math, Physics and Mind," I know, seem mundane, but I don't see the physical world as completely independent of humans.

          What am I missing? Many scientists say that humans adhere to the ERH concept.

          Jim

            Dear Tom,

            I am having an awful time with my credentialed fellow essayist. Several of them have reported my post as being inappropriate and had it removed.Thank you for your gracious humorous response to my comment.

            Thankfully,

            Joe Fisher

            Joe, you're not wrong. There's just no possible framework in which you could be proved right, that isn't self-referential.

            As Popper said, "All life is problem solving." The problem here is that life can't apparently communicate with sentient life other than by using abstract symbols and signals. How do you know, in fact, that you aren't communicating with an abstract being (me) through the abstract symbols on your keyboard that you are using? How do you know that I am 'real'?

            I don't know your level of knowledge or interest in philosophy or philosophical problems; however, if you agree with Wittgenstein's view, there are no philosophical problems at all -- just "language games and forms of life." At the end of the day, that may be a great truth, and it's still a philosophy I reject outright -- for the same reason that I reject your claim that the world includes no abstractions:

            Your conclusions, and Wittgenstein's, are based on inductive inference -- "Seeing is believing."

            I am a rationalist, though. In order to solve a problem, one must identify it -- even a guess is good -- and find the logical correspondence between the problem and its solution in order to consider it solved. I quote J. Bronowski often: "All science is the search for unity in hidden likenesses."

            Rationalism unites the world. Inductive inference divides it.

            All best,

            Tom

            Well, Jim, all I can say is that if you agree with Max's ERH table (slide 14 in this PowerPoint: www.fqxi.org/iceland/images/Iceland%20Talks/tegmark.ppt) you'll find my view at the extreme of "less baggage."

            I am a rationalist. An external reality and metaphysical realism are fundamental assumptions.

            Thanks for the note. I'll get to your essay when I can.

            Best,

            Tom

            Hi Michael,

            I'm ashamed of myself that I've had your book for a couple of years now, and haven't penetrated it -- though I know we have so many ideas in common.

            Please let me beg off commenting until I read your essay -- and thanks for dropping by!

            Till later, all best,

            Tom

            Dear Tom,

            "All science is the search for unity in hidden likenesses." If the abstract likenesses are hidden, how are you going to prove what they are likenesses of? There are no hidden abstract likenesses in reality." Therefore, all of science as you know it is erroneous. My contentions that real light is the only stationary substance in the real Universe and there is no physical space show that it is reality that is unified.

            Warm Regards,

            Joe Fisher

            Joe, you're all territory and no map. You can never be lost; neither, though, is there anywhere to go. Nor is there any science.

            Tom,

            Reality does not need a map. Because all surfaces travel at the same constant speed, land maps and blueprints can be accurately drawn.

            Joe

            That's where you're wrong, Joe. It doesn't mean anything to say that "surfaces travel at the same constant speed" -- because all motion is relative, as we've known since Mach wrote The Science of Mechanics in the 19th century.

            When you walk on a surface -- the ground -- is the surface traveling at the same constant speed as the surface of your feet that meet the ground? You wouldn't be going anywhere, would you? -- imagine that you are on a treadmill turning at the same speed as your stride, in the opposite direction; you would be walking "in place" relative to the surface of the treadmill. Have you been on a moving sidewalk at the airport? -- if the sidewalk is moving at say, 5 mph relative to the floor, and you are walking in the same direction as the mover at 5 mph -- are you not moving at 10 mph relative to the floor? If you dismount the sidewalk and stand still on the floor, are you not at rest relative to the floor?

            You want to say the floor is carrying the surface of your feet along at a speed constant with all other surfaces in nature -- in which case, nothing moves, ever. Not you, your feet, or the floor. Which contradicts your claim, "all surfaces travel at the same constant speed."

            "Reality," the way you are using it, only amounts to the old saying, "Wherever I go, there I am." Yes, that doesn't need a map, though it also contributes nothing to our knowledge of the territory. It isn't science's idea of reality.